Basketball Scoring Problem: Solve for (a+4) Close-Range Shots with 56 Total Points

A basketball player scores 3 points for each long-range shot and 2 points for each close-range shot.

He scores a total of 8 long-range shots and $a+4$ close-range shots.

How many shots does he score in total if he gets 56 points?

To solve this problem, we'll follow these steps:

• Step 1: Calculate the total points from long-range shots.
• Step 2: Formulate an equation for total points scored.
• Step 3: Solve for unknown $a$ using algebra.
• Step 4: Determine the total number of shots.

Now, let's work through each step:

Step 1: Compute points from long-range shots: The player makes 8 long-range shots, each worth 3 points. Thus, the total points from long-range shots are: $3 \times 8 = 24$

Step 2: Set up the total points equation. Let the points from close-range shots be denoted by $2 \times (a + 4)$. The total points scored is 56, so the equation becomes: $24 + 2 \times (a + 4) = 56$

Step 3: Solve for $a$. Expanding the equation, we get: $24 + 2a + 8 = 56$ Simplify the equation: $2a + 32 = 56$ Subtract 32 from both sides: $2a = 24$ Divide by 2 to solve for $a$: $a = 12$

Step 4: Calculate the total number of shots. Plugging $a = 12$ back into the expression for close-range shots, we get $a+4 = 16$. Therefore, the total shots are $8 + 16 = 24$.

Therefore, the solution to the problem is 24.